A study on network theory finds that the tipping point needed for a committed minority to win over the majority is just 10 percent

How do you topple a tyrant or popularize a foreign cuisine? According to a recent study in the journal Physical Review E, mobilizing an unyielding minority of 10 percent may be enough.

Scientists at Rensselaer Polytechnic Institute's Network Science and Technology Center created and analyzed various models of networks where a minority strived to overtake the majority's opinion. They found that three conditions are key: a majority that is flexible with their views, a minority that is intractable, and a critical threshold wherein about a tenth of the population advocate the minority opinion. They also saw that the time it takes to reach social consensus drops dramatically as the minority grows past this tipping point, a phenomenon they observed in the growth of anti-government sentiment in Tunisia and Egypt.

"I'd hesitate to reduce the spread of sushi in America to a formula." — Trevor Corson

"The governments of these two countries survived for decades in the past, despite more or less visible opposition," says coauthor and center director Boleslaw Szymanski. "Yet last winter, they were toppled in a matter of months."

The researchers saw this sudden power shift play out regardless of the network's structure. For a complete graph where each entity or node was connected with all the other nodes in the network (i.e. a small village where everyone knows each other), a staunch minority of 9.79 percent was enough to precipitate social agreement. For other graphs, including one where each node was connected to the same limited number of nodes and another where a select few were more connected than others, this critical threshold was no lower than seven percent. "Within the assumptions of our model," says Szymanski, "one can safely assume that 10 percent is an upper bound."

The study's implications on opinion dynamics are clear, says Albert-László Barabási, the author of the network-theory tome Linked: "Minorities can prevail only if they strive to become less of a minority," he says, "by turning a small fraction of the population into steadfast supporters of their cause." He adds that, though these models are simplified, they capture the essential features of opinion formation and are "crucial for a better understanding of the political and social landscape."

Andrea Baronchelli, a complex-systems scientist in Barcelona's Universitat Polit`ecnica de Catalunya, agrees. "It's important to point out the minimal ingredients that may originate a given phenomenon, with no pretension to claim that this is necessarily how things go," he says. "This suggests that the minority should convince new people to join them before worrying about convincing the whole world. Once they reach the critical size, the [network] dynamics will do the rest." He also notes that the study's demonstration of "the old saying that in a negotiation process the less reasonable will eventually prevail" at the societal level is particularly brilliant.

The researchers caution against indiscriminately applying the study's findings, however. They say the influence of the stubborn Tea Party members on the debt-ceiling resolution is different, for instance, since it involved two polarized parties, the Republicans and Democrats, where neither was considered a clear minority or majority to begin with. They also say that their study does not explain recent incidents in Libya and Syria. "Strongly committed members of the majority who are pro-government are not present in our model, nor is the brute force suppression of minority opinion," says Szymanski, who adds that earlier events in Egypt and Tunisia may have also served as an "external influence." Andrew Binder, a communication professor at North Carolina State University, says the civil rights movement, one of the authors' examples, may not fit as well. "We'd have to assume that 10 percent of African-American citizens were randomly distributed throughout the U.S. population," he says, "and this was clearly not the case."

As with most models, the scientists simplified variables and conditions to allow for analysis. Unlike real-world conversations, for example, the exchanges among the nodes in the networks involved pure opinions. Those in the network could only express agreement or disagreement with a certain position, and were unable to share grayer sentiments. Members who held the unpopular view were also spread randomly in the networks. And, it only took two interactions with holders of the same opinion to convert a member of the majority party: one to introduce the idea and another to drive it home. Perhaps most importantly, minority members were unwavering. "If they weren't intractable," explains coauthor Sameet Sreenivasan, "the model dynamics would quickly result in the wiping out of the minority opinion."

The authors note that there are historical events where the critical-threshold rule appears to be at work, such as the suffragette movement in the early 20th century. They share that, although not covered in their paper, the popularization of sushi in America may be due to the power of social networks as well. "Clearly, the committed individuals in this case were Japanese immigrants to Los Angeles who mingled with the locals and influenced their tastes," says Szymanski. Beyond Los Angeles, though, Sreenivasan says a second group of committed individuals &mdash; dieters and proselytizers of the organic food movement &mdash; may have helped. Sasha Issenberg bears this out in his book The Sushi Economy:

To most Americans, fish was something that could be canned, battered, fried, grilled, steamed, boiled, roasted &mdash; but certainly not served raw.... [During the post-war years, only in Los Angeles could] descendants of first-wave immigrants mingle with pop-culture tastemakers, and American health nuts with Japanese corporate expats. The one thing they all seemed able to agree on was lunch.... These elements &mdash; open-mindedness towards foreign cuisine, health consciousness, an aestheticization of natural foods and a belief in the perfectibility of the human physique through diet &mdash; mixed perfectly in Southern California.

Still, Trevor Corson, the author of The Story of Sushi, has some reservations. "Based on my research, there were many factors and variables that affected the adoption of sushi in the U.S.," he says, noting that entrepreneurial chefs from Japan, Hollywood stars, and government dietary recommendations also played a part. "I'd hesitate to reduce the spread of sushi in America to a mathematical formula."

Szymanski may have no such qualms about boiling down human phenomenon into numbers and graphs. For his team's future network models, he is interested in incorporating real-world data from social psychologists. "We welcome collaborations," he says. "Our research is open, basic, and fundamental."

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